Finite Group Databasebeta

← Group #68129

Character table — Group #68129

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size1111222222222244444444446666888888888888888812121212121224242424
order1222223444466666888812121212444444881212121224242424242424244488882488
χ1111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ61111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111
χ71111111111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111
χ81111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1
χ91111111-1-1-1-111111ii−i−i-1-1-1-111-1-11-1i−i-1-111ii−i−iii−i−i1-1ii−i−i1-1i−i
χ101111111-1-1-1-111111ii−i−i-1-1-1-111-1-1-11−ii11-1-1ii−i−i−i−iii1-1ii−i−i-11−ii
χ111111111-1-1-1-111111ii−i−i-1-1-1-1-1-1111-1i−i-1-111ii−i−iii−i−i-11−i−iii-11−ii
χ121111111-1-1-1-111111ii−i−i-1-1-1-1-1-111-11−ii11-1-1ii−i−i−i−iii-11−i−iii1-1i−i
χ131111111-1-1-1-111111−i−iii-1-1-1-111-1-11-1−ii-1-111−i−iii−i−iii1-1−i−iii1-1−ii
χ141111111-1-1-1-111111−i−iii-1-1-1-111-1-1-11i−i11-1-1−i−iiiii−i−i1-1−i−iii-11i−i
χ151111111-1-1-1-111111−i−iii-1-1-1-1-1-1111-1−ii-1-111−i−iii−i−iii-11ii−i−i-11i−i
χ161111111-1-1-1-111111−i−iii-1-1-1-1-1-111-11i−i11-1-1−i−iiiii−i−i-11ii−i−i1-1−ii
χ17222222-12222-1-1-1-1-12222-1-1-1-100002222-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ18222222-12222-1-1-1-1-12222-1-1-1-10000-2-2-2-21111-1-1-1-111110000000000
χ19222222-12222-1-1-1-1-1-2-2-2-2-1-1-1-1000022-2-2-1-1-1-1111111110000000000
χ20222222-12222-1-1-1-1-1-2-2-2-2-1-1-1-10000-2-22211111111-1-1-1-10000000000
χ21222222-1-2-2-2-2-1-1-1-1-12i2i−2i−2i111100002-22i−2i11-1-1−i−iii−i−iii0000000000
χ22222222-1-2-2-2-2-1-1-1-1-12i2i−2i−2i11110000-22−2i2i-1-111−i−iiiii−i−i0000000000
χ23222222-1-2-2-2-2-1-1-1-1-1−2i−2i2i2i111100002-2−2i2i11-1-1ii−i−iii−i−i0000000000
χ24222222-1-2-2-2-2-1-1-1-1-1−2i−2i2i2i11110000-222i−2i-1-111ii−i−i−i−iii0000000000
χ252222-2-2222-2-2222-2-2000022-2-222220000000000000000-2-200000000
χ262222-2-2222-2-2222-2-2000022-2-2-2-2-2-200000000000000002200000000
χ272222-2-22-2-222222-2-20000-2-22222-2-20000000000000000-2200000000
χ282222-2-22-2-222222-2-20000-2-222-2-22200000000000000002-200000000
χ292-22-22-222i−2i2i−2i-22-22-200002i−2i2i−2i00000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ302-22-22-222i−2i2i−2i-22-22-200002i−2i2i−2i0000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ312-22-22-22−2i2i−2i2i-22-22-20000−2i2i−2i2i0000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ322-22-22-22−2i2i−2i2i-22-22-20000−2i2i−2i2i00000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ332-22-2-2222i−2i−2i2i-22-2-222ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132i−2i−2i2i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000
χ342-22-2-2222i−2i−2i2i-22-2-22−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132i−2i−2i2i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000
χ352-22-2-222−2i2i2i−2i-22-2-22−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2i2i2i−2i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000
χ362-22-2-222−2i2i2i−2i-22-2-222ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2i2i2i−2i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000
χ372-22-2-22-12i−2i−2i2i1-111-12ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−iii−i00000000−i3i33−3−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ382-22-2-22-12i−2i−2i2i1-111-12ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−iii−i00000000i3−i3−33−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ392-22-2-22-12i−2i−2i2i1-111-1−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−iii−i00000000−i3i33−3ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ402-22-2-22-12i−2i−2i2i1-111-1−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−iii−i00000000i3−i3−33ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ412-22-2-22-1−2i2i2i−2i1-111-1−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23i−i−ii00000000−i3i3−33ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ422-22-2-22-1−2i2i2i−2i1-111-1−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23i−i−ii00000000i3−i33−3ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ432-22-2-22-1−2i2i2i−2i1-111-12ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23i−i−ii00000000−i3i3−33−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ442-22-2-22-1−2i2i2i−2i1-111-12ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23i−i−ii00000000i3−i33−3−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ454444-4-4-244-4-4-2-2-2220000-2-222000000000000000000000000000000
χ464444-4-4-2-4-444-2-2-222000022-2-2000000000000000000000000000000
χ4744-4-40040000-4-440000000000004i−4i00000000000000000000000000
χ4844-4-40040000-4-44000000000000−4i4i00000000000000000000000000
χ494-44-44-4-24i−4i4i−4i2-22-220000−2i2i−2i2i000000000000000000000000000000
χ504-44-44-4-2−4i4i−4i4i2-22-2200002i−2i2i−2i000000000000000000000000000000
χ514-4-4400400004-4-400000000004i−4i0000000000000000000000000000
χ524-4-4400400004-4-40000000000−4i4i0000000000000000000000000000
χ5388-8-800-4000044-40000000000000000000000000000000000000000
χ548-8-8800-40000-4440000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.